geo (finals)

please help! i don't get these problems at all!
a(4,3) b(7,4) and c(5,2) are midpoints of a triangle. find the coordinates for the vertices of the triangle!

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asked by Skylar
  1. Let the vertices be A, B, and C, where A is the vertex opposite a(4,3) etc.

    let's work on the x's first,
    let the corresponding x's be p, q, and r

    (p+q)/2 = 7
    p + q = 14 -- #1
    in the same way...
    p + r = 10 -- #2
    q + r = 8 -- #3

    subtract #1 - #2
    q - r = 4
    add that to #3
    2q = 12
    q = 6
    then r = 2
    and p = 8

    now do the y's the same way.

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    posted by Reiny
  2. wait what? I'm a bit confused here. so (4,3) would be on CB?

    whats does corresponding x mean? and how did x appear?

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    posted by SKipper
  3. Yes, (4,3) is on CB
    (5,2) on AB and (7,4) on AC

    I let the points be A(p, ?), B(q, ?) and C(r, ?)

    I then followed the definition of finding midpoints.
    Don't you add up the x values , then divide by 2 , to get the x of the midpoint?

    Pick your own values for the y's, and follow the same method.

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    posted by Reiny
  4. Sorry, but I got lost here...


    I let the points be A(p, ?), B(q, ?) and C(r, ?)

    ^what does this?



    I then followed the definition of finding midpoints.
    Don't you add up the x values , then divide by 2 , to get the x of the midpoint?

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    posted by SKipper

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